Simplify Square Root of 269

What is the square root of 269 in its simplest radical form? To be more specific, we have created an illustration below showing what we want to calculate. Our goal is to make "A" outside the radical (√) as large as possible, and "B" inside the radical (√) as small as possible.

√269 = A√B

Unfortunately, the square root of 269 cannot be simplified. Thus, here is the answer to the square root of 269 in its simplest form:

√ 269 = √ 269

Here are two different methods we used to determine why the square root of 269 cannot be simplified.

1) To be able to simplify the square root of 269, one of the factors of 269 other than 1 must be a perfect square. The factors of 269 are 1 and 269. Since none of these factors are perfect squares, the square root of 269 cannot be simplified.

2) To be able to simplify the square root of 269, all the prime factors of 269 cannot be unique. When we did prime factorization of 269, we found that 269 equals 269. Since all the prime factors are unique, the square root of 269 cannot be simplified.

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